• 대한수학회보
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• 제30권1호
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• pp.99-107
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• 1993

A vector space K with scalar product <.,.> is called a Krein space if it can be decomposed as a northogonal sum of a Hilbert space and an anti-space of a Hilbert space. The space K induces a Hilbert space $K_{J}$ in the inner product <.,.> $K_{J}$=<.,.>K, where $J^{2}$=I. the eigenspaces of J are denoted by $K^{+}$$_{J}$, which is a Hilbert space and $K^{-}$$_{J}$, which is an anti-space of a Hilbert space. Then the Krein space K is the orthogonal sum of $K^{+}$$_{J}$ and $K^{-}$$_{J}$. Such a decomposition of K is called a fundamental decomposition. In general, fundamental decompositions are not unique. The norm of the Hilbert space depends on the choice of a fundamental decomposion, but such norms are equivalent. The topology generated by these norms is called the strong or Mackey topology of K. It is used to define all topological notions on the Krein space K with respect to this topology. The Pontryagin index of a Krein space is the dimension of the antispace of a Hilbert space in any such decomposition. the dimension does not depend on the choice of orthogonal decomposition. A Krein space is called a Pontryagin space if it has finite Pontryagin index.dex.yagin index.dex.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.291-298
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• 2006

A parallelized topology design optimization method is developed on a distributed memory system. The parallelization is based on a domain decomposition method and a boundary communication scheme. For the finite element analysis of structural responses and design sensitivities, the PCG method based on a Krylov iterative scheme is employed. Also a parallelized optimization method of optimality criteria is used to solve large-scale topology optimization problems. Through several numerical examples, the developed method shows efficient and acceptable topology optimization results for the large-scale problems.

• Journal of Communications and Networks
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• 제14권3호
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• pp.319-335
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• 2012

In this study, we design an applicable model enabling internet protocol television (IPTV) service providers to use a virtual network (VN) for IPTV service delivery. The model addresses the guaranteed service delivery, cost effectiveness, flexible control, and scalable network infrastructure limitations of backbone or IP overlay-based content networks. There are two major challenges involved in this research: i) The design of an efficient, cost effective, and reliable virtual network topology (VNT) for IPTV service delivery and the handling of a VN allocation failure by infrastructure providers (InPs) and ii) the proper approach to reduce the cost of VNT recontruction and reallocation caused by VNT allocation failure. Therefore, in this study, we design a more reliable virtual network topology for solving a single virtual node, virtual link, or video server failure. We develop a novel optimization objective and an efficient VN construction algorithm for building the proposed topology. In addition, we address the VN allocation failure problem by proposing VNT decomposition and reconstruction algorithms. Various simulations are conducted to verify the effectiveness of the proposed VNT, as well as that of the associated construction, decomposition, and reconstruction algorithms in terms of reliability and efficiency. The simulation results are compared with the findings of existing works, and an improvement in performance is observed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제3권6호
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• pp.667-681
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• 2009

We describe a method to decompose a cube with trilinear interpolation into a collection of tetrahedra with linear interpolation, where the isosurface topology is preserved for all isovalues during decomposition. Visualization algorithms that require input scalar data to be defined on a tetrahedral grid can utilize our method to process 3D rectilinear data with topological correctness. As one of many possible examples, we apply the decomposition method to topologically accurate tetrahedral mesh extraction of an interval volume from trilinear volumetric imaging data. The topological correctness of the resulting mesh can be critical for accurate simulation and visualization.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권1호
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• pp.145-164
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• 2014

Network virtualization provides a promising tool to allow multiple heterogeneous virtual networks to run on a shared substrate network simultaneously. A long-standing challenge in network virtualization is the Virtual Network Embedding (VNE) problem: how to embed virtual networks onto specific physical nodes and links in the substrate network effectively. Recent research presents several heuristic algorithms that only consider single topological attribute of networks, which may lead to decreased utilization of resources. In this paper, we introduce six complementary characteristics that reflect different topological attributes, and propose three topology-aware VNE algorithms by leveraging the respective advantages of different characteristics. In addition, a new KS-core decomposition algorithm based on two characteristics is devised to better disentangle the hierarchical topological structure of virtual networks. Due to the overall consideration of topological attributes of substrate and virtual networks by using multiple characteristics, our study better coordinates node and link embedding. Extensive simulations demonstrate that our proposed algorithms improve the long-term average revenue, acceptance ratio, and revenue/cost ratio compared to previous algorithms.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.647-650
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• 2009

For a bounded operator T = $U{\mid}T{\mid}$ (polar decomposition), we consider a transform b $\widehat{T}$ = ${\mid}T{\mid}U$ and discuss the convergence of iterated transform of $\widehat{T}$ under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.

• 대한조선학회논문집
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• 제47권1호
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• pp.58-66
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• 2010

Topology design optimization is a method to determine the optimal distribution of material that yields the minimal compliance of structures, satisfying the constraint of allowable material volume. The method is easy to implement and widely used so that it becomes a powerful design tool in various disciplines. In this paper, a large-scale topology design optimization method is developed using the efficient adjoint sensitivity and optimality criteria methods. Parallel computing technique is required for the efficient topology optimization as well as the precise analysis of large-scale problems. Parallelized finite element analysis consists of the domain decomposition and the boundary communication. The preconditioned conjugate gradient method is employed for the analysis of decomposed sub-domains. The developed parallel computing method in topology optimization is utilized to determine the optimal structural layout of human powered vessel.

• 대한수학회논문집
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• 제9권4호
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• pp.847-852
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• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operator on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$.

• 한국정밀공학회지
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• 제23권1호
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• pp.174-184
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• 2006

In order to fill the holes with complex shapes in the large polygon model, a new approach which is based on the implicit surface interpolation method combined with domain decomposition method is presented. In the present study, a surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In the method an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$ The generated surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In this paper the well-known domain decomposition method is used in order to treat the large polygon model. The global domain of interest is divided into smaller domains where the problem can be solved locally. LU decomposition method is used to solve a set of small local problems and their local solutions are combined together using the weighting coefficients to obtain a global solution. In order to show the validity of the present study, various hole fillings are carried out fur the large and complex polygon model of arbitrary topology.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권1호
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• pp.66-76
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• 2012

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.